Question

Estimate how many terms in the sum are
needed to calculate int sin x dx from 1.3 to 3.3 (for example, with accuracy of 10^3), using Midpoint rule, Trapezoid rule, and Simpson’s rule.

Answer 1

Use the error bound equations for each technique, and that will give you what you are looking for. I'm pretty sure that they are covered in the chapter(s) you are working with, and on this site, writing all of those equations is extra tedious. Check out the literature in the chapter and you should be alright.

Answer 2

The question is all about showing you that Simpson's Rule is better to use for approximation. You use less terms to get a more accurate answer.